Need some help...
Let the ring of gaussian integers.
1)Show that
( means the ideal generated by )
2)Prove that the ideal on the right is prime.
Thank you folks!
thereīs one thing thatīs not clear to me:
Iīve just proved that , which means that is isomorphic to , which is a field.
That allows me to say that the ideal is prime?
As far as Iīm concerned, the quotient of a ring by a prime ideal is a domain.
Iīm kind of confused with that...
But the help was very helpful
And I have one more question: is the product of two ideals the set of all the products of the elements of each ideal??
Thanks!
that means the ideal is maximal and we know that every maximal ideal is prime.
no. if and are two ideals, then however, for example, if you want to prove that where is an ideal, then you only need to prove that
And I have one more question: is the product of two ideals the set of all the products of the elements of each ideal??
for all